Exams › JEE Main › Maths

For an arbitrary vector a, the quantity (a × î)² + (a × ĵ)² + (a × k̂)² is equal to

1. 3a²
2. a²
3. 2a²
4. 4a²

Correct answer: 2a²

Solution

The expression represents the sum of the squares of the magnitudes of the cross products of vector a with the unit vectors i, j, and k. Each term contributes a factor of a², and due to the properties of cross products, the total simplifies to 2a².

Related JEE Main Maths questions

• If ((â × b̂) × (ĉ × d̂)) · (â × d̂) = 0, which statement must always hold?
• For four points A, B, C and D in space, if the dot product of vectors AB and CD is given by k times [|AD|² + |BC|² - |AC|² - |BD|²], then what is the value of k?
• Three vectors →a, →b and →c have magnitudes |→a| = 4, |→b| = 4 and |→c| = 2. If →a is orthogonal to (→b + →c), →b is orthogonal to (→c + →a), and →c is orthogonal to (→a + →b), then the magnitude of (→a + →b + →c) is:
• The position vectors of the vertices A, B and C of triangle ABC are 4î + 7ĵ + 8k̂, 2î + 3ĵ + 4k̂ and 2î + 5ĵ + 7k̂ respectively. The position vector of the point where the internal bisector of angle A intersects BC is
• Let a=a₁î+a₂ĵ+a₃k̂, b=b₁î+b₂ĵ+b₃k̂, and c=c₁î+c₂ĵ+c₃k̂ be three non-zero vectors. Suppose c is a unit vector perpendicular to both a and b. If the angle between a and b is π/6, then the value of |[a₁, a₂, a₃; b₁, b₂, b₃; c₁, c₂, c₃] | is
• Let a, b, and c be three vectors that are not in the same plane. Define p = (b × c)/([abc]), q = (c × a)/([abc]), and r = (a × b)/([abc]). Then the value of (a+b)·p + (b+c)·q + (c+a)·r is

⚔️ Practice JEE Main Maths free + battle 1v1 →